Locomotion systems can be used in various applications, such as robotics. Aspects relating to locomotion in robotics are concerned with designing powered mechanisms that allow robots to move in their environments. The present description focuses on terrestrial locomotion, which is concerned with moving on land upon rigid structures (such as the tops of desks and tables or the ground) and is distinct from aerial, aquatic or other types of locomotion. From another perspective, locomotion can be divided into indoor and outdoor applications, which usually impose distinct requirements on the locomotion system that is built. These include:                robustness against obstacles in the environment, or the inherent structure of the environment, such as natural rough terrain;        robustness against external disturbances;        mechanical durability and complexity;        monetary cost, affordability;        power consumption, efficiency;        precision;        physical compactness, size and shape; and        kinematic constraints, e.g. holonomic vs. non-holonomic.        
Considering these requirements, the locomotion literature converged to two distinct types of systems, which are legged and wheeled systems. Legged systems generally offer high robustness against rough environments at the cost of a higher number of degrees of freedom (DOFs), more complexity and more cost. Therefore, they address mainly, though not exclusively, outdoor scenarios. On the other hand, wheeled systems generally offer less robustness against rough environments (or are not concerned at all with such environments) but are much simpler and more efficient. As a result, they are often preferred, though again not exclusively, when dealing with indoor scenarios.
The locomotion systems considered in the present description preferably fulfill at least some of the following requirements:                holonomic motion to allow haptic feedback instantaneously in any direction (in x, y and/or θ) when the locomotion system is grasped;        mechanical robustness against being externally driven;        design composed of simple, few and preferably off-the-shelf components in order to minimize custom manufacturing steps to ease the transition from a prototype design to a consumer device design;        as low cost, as possible; and        compact enough geometry so that the system physically fits inside a handheld volume allowing it to be grasped entirely.        
Given the above constraints, legged systems are excluded from consideration and only wheeled systems, which allow three DOF holonomic motions on a substantially horizontal plane, are considered in the following.
It is trivially true that for holonomic motion (requiring instantaneous motion capability toward an arbitrary direction in any configuration), wheels with at least two DOF are required. Here, a large design space exists for the individual and collective kinematics of these wheels. The first prominent example is actively steered wheels that feature two orthogonal DOFs that are both driven. These are simple to build and operate, but require that some time is spent to turn the wheels into the direction of motion if the desired direction changes discontinuously. Thus, these systems are not “instantaneously” omnidirectional. If the wheel is made a caster, it is possible to make omnidirectionality instantaneous. However, some driving elements must still remain on the link that houses the wheel itself in order to ensure that the wheel is driven. This increases complexity and decreases mechanical robustness since this link must itself also rotate to ensure control over the other DOF.
Swedish wheels, also known as Mecanum wheels, omnidirectional wheels or omni wheels, are a second prominent example. These wheels feature two orthogonal or 45° oriented DOFs, one of which is driven while the other one is free to ensure low-friction backdrivability. These can move instantaneously toward any direction but are relatively less simple to build, typically less robust against obstacles and suffer from undesirable vibrations due to discontinuous contact points with the ground.
Ball wheels are a final prominent example, which feature two (or three) non-collinear DOFs, at least one of which is driven and the rest is/are free. Since the spherical wheel appears to have the exact same surface no matter what its orientation is, ball wheels can be made truly isotropic, ensuring the smoothest possible motion. However, they are typically difficult to build and design such that they ensure efficient locomotion. Compared to omni wheel drives, ball drives offer significantly better vibration robustness and easier miniaturization when components of similar sizes are considered. These are important features e.g. for palm-sized robots that should be free of unintentional vibrations, which would disturb the haptic feedback. Ball wheel drives typically use rotating contact elements to drive the ball wheel. However, the contact force between the drive roller and the ball wheel is a challenge, which is conventionally solved by external spring-loaded elements. However, this increases complexity and cost of the system. It is to be noted that the above considerations are not restricted to the field of robotics, but are also valid in fields other than robotics.